Related papers: The Wishart short rate model
We consider a class of conditional forward-backward diffusion models for conditional generative modeling, that is, generating new data given a covariate (or control variable). To formally study the theoretical properties of these…
Wishart random matrices are often used to model multivariate systems in physics, finance, biology and wireless communication. Extreme value statistics, such as those of the smallest eigenvalue, can be used to test the accuracy of the model.…
We investigate the effect of directed short and long range connections in a simple model of small world network. Our model is such that we can determine many quantities of interest by an exact analytical method. We calculate the function…
We reverse-engineer the equilibrium construction process of asset prices in order to obtain returns which depend on firm characteristics, possibly in a linear fashion. One key requirement is that agents must have demands that rely…
We develop a stochastic calculus that makes it easy to capture a variety of predictable transformations of semimartingales such as changes of variables, stochastic integrals, and their compositions. The framework offers a unified treatment…
This paper investigates the asymptotic behavior of suitably time-modulated Hawkes processes with heavy-tailed kernels in a nearly unstable regime. We show that, under appropriate scaling, both the intensity processes and the rescaled Hawkes…
In 'A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options', Heston proposes a Stochastic Volatility (SV) model with constant interest rate and derives a semi-explicit valuation formula.…
Pervasive cross-section dependence is increasingly recognized as a characteristic of economic data and the approximate factor model provides a useful framework for analysis. Assuming a strong factor structure where $\Lop\Lo/N^\alpha$ is…
Marginal expected shortfall is unquestionably one of the most popular systemic risk measures. Studying its extreme behaviour is particularly relevant for risk protection against severe global financial market downturns. In this context,…
Matrix Dirichlet processes, in reference to their reversible measure, appear in a natural way in many different models in probability. Applying the language of diffusion operators and the method of boundary equations, we describe Dirichlet…
We provide a unified framework for modeling LIBOR rates using general semimartingales as driving processes and generic functional forms to describe the evolution of the dynamics. We derive sufficient conditions for the model to be…
In power system operation, characterizing the stochastic nature of wind power is an important albeit challenging issue. It is well known that distributions of wind power forecast errors often exhibit significant variability with respect to…
Capretta's delay monad can be used to model partial computations, but it has the "wrong" notion of built-in equality, strong bisimilarity. An alternative is to quotient the delay monad by the "right" notion of equality, weak bisimilarity.…
In reinforcement learning, it is typical to use the empirically observed transitions and rewards to estimate the value of a policy via either model-based or Q-fitting approaches. Although straightforward, these techniques in general yield…
An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…
Using a character expansion method, we calculate exactly the eigenvalue density of random matrices of the form M^\dagger M where M is a complex matrix drawn from a normalized distribution P(M) ~ exp(-\Tr(A M B M^\dagger) with A and B…
This paper deals with an extension of the so-called Black-Scholes model in which the volatility is modeled by a linear combination of the components of the solution of a differential equation driven by a fractional Brownian motion of Hurst…
Earlier we proposed the stochastic point process model, which reproduces a variety of self-affine time series exhibiting power spectral density S(f) scaling as power of the frequency f and derived a stochastic differential equation with the…
This note studies a certain stochastic evolution equation in the space of probability measures, including existence and uniqueness results. A solution of this equation gives rise, in a natural way, to an interest rate term structure model,…
The empirical likelihood inference is extended to a class of semiparametric models for stationary, weakly dependent series. A partially linear single-index regression is used for the conditional mean of the series given its past, and the…